Problems & Puzzles: Puzzles

Puzzle 594. 999997600699 Anton Vrba sent the following nice puzzle: The 12 digit prime 999997600699 has a special property, it can hide in a string of ones, threes, sevens or nines and remain prime.   1919191919171610101619191 3939393939373630303639393 7979797979777670707679797 9999999999979690909699999 Q. Can you find a larger prime than 999997600699  and the corresponding four primes produced? (See this curio too)

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Contributions cam from Emmanuel Vantieghem, Hakan Summakoğlu & Paul Schmidt.

Emmanuel wrote:

Here is the biggest prime with the desired property :

99999999999999999989777141 which give rise to the primes :

19191919191919191919191919191919191918191717171114111
39393939393939393939393939393939393938393737373134313
79797979797979797979797979797979797978797777777174717
99999999999999999999999999999999999998999797979194919

(all proved prime by Mathematica). I'm sure there are infinitely many such primes.

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Hakan wrote:

4554261531293
141515141216111513111219131
343535343236313533313239333
747575747276717573717279737
949595949296919593919299939

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Paul wrote

9999999999999999999999999999999990000843608321 (46 digits)

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